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<p>In this paper, we consider least squares estimator for an unknown parameter in the drift coeffcient of path-distribution dependent stochastic differential equation driven by fractional Brownian motions with Hurst parameter <i>H</i> ∈ (1/2, 1). Based on <i>n</i> (<i>n</i> ∈ ℕ) discrete time observations of the stochastic differential equation, the estimator is shown to be convergent to the true value as the small dispersion parameter <i>ε</i> → 0 and <i>n</i> → ∞. Moreover, we obtain the asymptotic distribution of the estimator. At last, we provide an example to illustrate our results and give the numerical simulations to support our theoretical analysis.</p>

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Least Squares Estimation for Path-distribution Dependent Stochastic Differential Equations Driven by Fractional Brownian Motions

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Guang-jun Shen,
  • Jiang-peng Wang,
  • Mei-meng Ye,
  • Huan Zhou

摘要

In this paper, we consider least squares estimator for an unknown parameter in the drift coeffcient of path-distribution dependent stochastic differential equation driven by fractional Brownian motions with Hurst parameter H ∈ (1/2, 1). Based on n (n ∈ ℕ) discrete time observations of the stochastic differential equation, the estimator is shown to be convergent to the true value as the small dispersion parameter ε → 0 and n → ∞. Moreover, we obtain the asymptotic distribution of the estimator. At last, we provide an example to illustrate our results and give the numerical simulations to support our theoretical analysis.